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Improving The Floris Wind Plant Model For Compatibility With Gradient-Based Optimization, Jared Thomas, Pieter Gebraad, Andrew Ning Aug 2017

Improving The Floris Wind Plant Model For Compatibility With Gradient-Based Optimization, Jared Thomas, Pieter Gebraad, Andrew Ning

Faculty Publications

The FLOw Redirection and Induction in Steady-state (FLORIS) model, a parametric wind turbine wake model that predicts steady state wake characteristics based on wind turbine position and yaw angle, was developed for optimization of control settings and turbine locations. This paper provides details on the recent changes made to the FLORIS model to make the model more suitable for gradient-based optimization. Changes to the FLORIS model were made to remove discontinuities and add curvature to regions of non-physical zero gradient. Exact gradients for the FLORIS model were obtained using algorithmic differentiation. A set of three case studies demonstrate that using …


Electrokinetically Operated Integrated Microfluidic Devices For Preterm Birth Biomarker Analysis, Mukul Sonker Aug 2017

Electrokinetically Operated Integrated Microfluidic Devices For Preterm Birth Biomarker Analysis, Mukul Sonker

Theses and Dissertations

Microfluidics is a vibrant and expanding field that has the potential for solving many analytical challenges. Microfluidics shows promise to provide rapid, inexpensive, efficient, and portable diagnostic solutions that can be used in resource-limited settings. Microfluidic devices have gained immense interest as diagnostic tools for various diseases through biomarker analysis. My dissertation work focuses on developing electrokinetically operated integrated microfluidic devices for the analysis of biomarkers indicative of preterm birth risk. Preterm birth (PTB), a birth prior to 37 weeks of gestation, is the most common complication of pregnancy and the leading cause of neonatal deaths and newborn illnesses. In …


Characterizing The Fate And Mobility Of Phosphorus In Utah Lake Sediments, Matthew Chambers Randall Aug 2017

Characterizing The Fate And Mobility Of Phosphorus In Utah Lake Sediments, Matthew Chambers Randall

Theses and Dissertations

An increasing number of lakes worldwide are impacted by eutrophication and harmful algal blooms due to nutrient inputs. Utah Lake is a unique eutrophic freshwater lake that is naturally shallow, turbid, and alkaline with high dissolved oxygen levels. Recently, the Utah Division of Water Quality has proposed a new limitation of phosphorus (P) loading to Utah Lake from wastewater treatment plants in an effort to mitigate eutrophication. However, reducing external P loads may not lead to immediate improvements in water quality due to the legacy pool of nutrients in lake sediments. The purpose of this study was to characterize the …


Miniaturization Of Linear Ion Traps And Ion Motion Study In A Toroidal Ion Trap Mass Analyzer, Ailin Li Aug 2017

Miniaturization Of Linear Ion Traps And Ion Motion Study In A Toroidal Ion Trap Mass Analyzer, Ailin Li

Theses and Dissertations

I describe the miniaturization of a linear-type ion trap mass spectrometer for possible applications in portable chemical analysis, and demonstrate the advantages of using lithographically patterned electrode plates in realizing an ion trap with dimension r0 less than 1 mm. The focus of the work was to demonstrate the viability and feasibility of the patterned electrode approach to trap miniaturization, and also to discover potential obstacles to its use. Planar ceramic substrates were patterned with metal electrodes using photolithography. Plates that were originally used in a linear trap with a half-spacing (r0) of 2.19 mm were positioned …


A General-Purpose Animation System For 4d, Justin Alain Jensen Aug 2017

A General-Purpose Animation System For 4d, Justin Alain Jensen

Theses and Dissertations

Computer animation has been limited almost exclusively to 2D and 3D. The tools for 3D computer animation have been largely in place for decades and are well-understood. Existing tools for visualizing 4D geometry include minimal animation features. Few tools have been designed specifically for animation of higher-dimensional objects, phenomena, or spaces. None have been designed to be familiar to 3D animators. A general-purpose 4D animation system can be expected to facilitate more widespread understanding of 4D geometry and space, can become the basis for creating unique 3D visual effects, and may offer new insight into 3D animation concepts. We have …


Analysis Of Differential Equations Applications From The Coordination Class Perspective, Omar Antonio Naranjo Mayorga Aug 2017

Analysis Of Differential Equations Applications From The Coordination Class Perspective, Omar Antonio Naranjo Mayorga

Theses and Dissertations

In recent years there has been an increasing interest in mathematics teaching and learning at undergraduate level. However, many fields are little explored; differential equations being one of these topics. In this study I use the theoretical framework of Coordination Classes to analyze how undergraduate mechanical engineering students apply their knowledge in the context of system dynamics and what resources and strategies they used; in this subject, students model dynamics systems based on Ordinary Differential Equations (ODEs). I applied three tasks in different contexts (Mechanical, Electrical and Fluid Systems) in order to identify what information was relevant for the students, …


Kyozaikenkyu: An In-Depth Look Into Japanese Educators' Daily Planning Practices, Matthew David Melville Aug 2017

Kyozaikenkyu: An In-Depth Look Into Japanese Educators' Daily Planning Practices, Matthew David Melville

Theses and Dissertations

This study is in response to the question about how Japanese educators achieve such a high quality of instruction. Considering the area of lesson study has opened the door to new ideas and concepts that are not well defined and too broad to understand. Kyozaikenkyu is an aspect of lesson study that has been said to be a crucial aspect to successful lesson study. Kyozaikenkyu is done on a daily basis by Japanese educators; however, there is very little written about this process in relevant literature. This study examines what Japanese educators do during their daily kyozaikenkyu, and why …


Role Of Molecular Chaperonin Cct And Its Co-Chaperone Phlp1 In The Assembly Of Mtor Complexes, Madhura Vinayak Dhavale Aug 2017

Role Of Molecular Chaperonin Cct And Its Co-Chaperone Phlp1 In The Assembly Of Mtor Complexes, Madhura Vinayak Dhavale

Theses and Dissertations

mTOR is the central kinase in biochemical pathways that regulate cellular growth, protein synthesis and cell survival. Deregulation of mTOR signaling results in uncontrolled cell proliferation and hence is implicated in various cancers and autoimmune diseases. mTOR functions through two distinct signaling complexes, called mTORC1 and mTORC2. CCT is a cytosolic chaperonin that assists in folding of several protein substrates. In these studies, we have identified two components of the mTOR complexes, mLST8 and Raptor, as substrates of CCT. We have performed biochemical and signaling studies which indicate that CCT is involved in assembly and signaling of mTOR complexes by …


Microwave-Promoted Iminyl Radical Fragmentations: A Practical And Efficient Method Of Functionalization, Mary Megan Jackman Aug 2017

Microwave-Promoted Iminyl Radical Fragmentations: A Practical And Efficient Method Of Functionalization, Mary Megan Jackman

Theses and Dissertations

We report a novel fragmentation and functionalization method using a cyclic iminyl radical. Formation of this radical occurs by microwave heating under mild conditions and short reaction times. The reaction avoids the use of explosive or toxic radical initiators and propagating agents. This reaction is versatile, with the ability to install two functional groups that are ultimately derived from a ketone in the substrate precursor. A variety of radical traps capable of forming both carbon-carbon bonds and carbon-heteroatom bonds have been tested, and the products are obtained in good yields. We demonstrate the power of this reaction by functionalizing complex …


Electrophilic Catalysis Using Heterobimetallic Complexes, Whitney Kaye Walker Aug 2017

Electrophilic Catalysis Using Heterobimetallic Complexes, Whitney Kaye Walker

Theses and Dissertations

Conventional ligand design in transition metal catalysis capitalizes on the ability of phosphorous, nitrogen, carbon, oxygen, and sulfur-based donors to modify the steric and electronic properties of a reactive metal center. Heterobimetallic transition metal complexes that contain a dative metal-metal bond provide a unique approach to ligand design where the reactivity of the metal center can be modified by metal-metal electronic communication. Our laboratory is interested in using the unique properties of heterobimetallic complexes to address significant limitations in current transition metal catalysis. My PhD work has focused on the ability of early/late transition metal heterobimetallic complexes to facilitate catalysis …


Ion Trap Miniaturization Considerations: Space-Charge Effects In Cylindrical Ion Traps And Misalignment Effects In A Two-Plate Linear Ion Trap, Yuan Tian Aug 2017

Ion Trap Miniaturization Considerations: Space-Charge Effects In Cylindrical Ion Traps And Misalignment Effects In A Two-Plate Linear Ion Trap, Yuan Tian

Theses and Dissertations

Portable mass spectrometers provide convenience for applications where conventional mass spectrometers are not suitable. However, a series of miniaturization issues show up in small mass spectrometers, specifically mass analyzers, that need to be thoroughly addressed before further miniaturization. The work in this dissertation focuses on miniaturization issues of ion trap mass analyzers. Space-charge is one of the major issues in small ion traps affecting their analytical performance. It limits ion trapping capacity when ion-ion repulsion causes spreading of a packet of ions. Simulation studies on the relationship between different trap dimensions and trapping capacity was done on a geometry-optimized cylindrical …


Microwave-Promoted Iminyl Radical Cyclizations For The Synthesis Of Azaheterocycles And The Total Synthesis Of Yaku'amide A, Yu Cai Aug 2017

Microwave-Promoted Iminyl Radical Cyclizations For The Synthesis Of Azaheterocycles And The Total Synthesis Of Yaku'amide A, Yu Cai

Theses and Dissertations

Two different research projects are described in this dissertation. The first one focuses on microwave-promoted iminyl radical cyclization for the formation of azaheterocycles which are embedded within numerous pharmaceuticals and biologically active natural products (such as clindamycin, eletriptan, moxiflaxin, etc.). We are quite interested in this project because of the significance of nitrogen-containing heterocycles as pharmaceuticals and organocatalysts combined with the need for safe, simple, and economical means of constructing them. We have successfully developed an efficient one-step synthesis of 2-acylpyrroles and diastereoselective dihydropyrroles from readily available oxime ether substrates. This remarkably efficient and environmentally friendly methodology should be useful …


Post-Translational Regulation Of Superoxide Dismutase 1 (Sod1): The Effect Of K122 Acylation On Sod1'S Metabolic Activity, Courtney Jean Banks Aug 2017

Post-Translational Regulation Of Superoxide Dismutase 1 (Sod1): The Effect Of K122 Acylation On Sod1'S Metabolic Activity, Courtney Jean Banks

Theses and Dissertations

Many mutations in superoxide dismutase 1 (SOD1) cause destabilization and misfolding of the protein and are implicated in amyotrophic lateral sclerosis. Likewise, a few post-translational modifications (PTMs) on SOD1 have been shown to cause the same phenotype. However, relatively few PTMs on SOD1 have been studied in depth and, in particular, very few studies have demonstrated how these PTMs affect SOD1's various biological roles. SOD1 is traditionally known for its role in reactive oxygen species (ROS)-scavenging but has also been found to have a few other biological roles, including transcription factor activity to promote genomic stability, preservation of cytoskeletal activity, …


Ground Reaction Forces Through A Range Of Speeds In Steeplechase Hurdling, James Brian Tracy Aug 2017

Ground Reaction Forces Through A Range Of Speeds In Steeplechase Hurdling, James Brian Tracy

Theses and Dissertations

The men's steeplechase event requires participants to jump over thirty-five 0.914-meter-tall obstacles, 4 rigid barriers and 1 fixed barrier followed by a 3.66-meter-long water pit per lap, over a 3000-meter distance. This study investigated the effect of increasing running velocity, through a range of 5.33 m/s to 6.66 m/s, on takeoff and landing ground reaction forces, for males during steeplechase hurdling using a force plate embedded under a track surface. Subjects completed 1 trial within each of 6 different pace ranges in a random order, once with a hurdle following the force plate to measure the takeoff ground reaction forces …


Advancements In The Understanding Of Nonlinear Optics And Their Use In Material Analysis, Shawn C. Averett Aug 2017

Advancements In The Understanding Of Nonlinear Optics And Their Use In Material Analysis, Shawn C. Averett

Theses and Dissertations

Adhesion, heterogeneous catalysis, electrochemistry, and many other important processes and properties are driven by interactions at surfaces and interfaces. Vibrational sum frequency generation spectroscopy (VSFG) is an increasingly popular analytical technique because it can provide information about the nature and physical orientation of functional groups at these surfaces and interfaces. Analysis of VSFG data can be complicated by the presence of SFG signal that is not associated with a resonant vibration. This nonresonant sum frequency generation (NR-SFG) signal can interfere with the resonant signal and influence the detected spectrum. Methods have been developed to remove NR-SFG signal; however, these methods …


Characterizing The Low Net-To-Gross, Fluviodeltaic Dry Hollow Member Of The Frontier Formation, Western Green River Basin, Wyoming, Scott Romney Meek Aug 2017

Characterizing The Low Net-To-Gross, Fluviodeltaic Dry Hollow Member Of The Frontier Formation, Western Green River Basin, Wyoming, Scott Romney Meek

Theses and Dissertations

The Frontier Formation in the Green River Basin of southwestern Wyoming consists of Late Cretaceous (Cenomanian-Turonian) marine and non-marine sandstones, siltstones, mudstones and coals deposited on the western margin of the Cretaceous Interior Seaway. Tight gas reservoirs exist in subsurface fluviodeltaic sandstones in the upper Frontier Formation (Dry Hollow Member) on the north-south trending Moxa Arch within the basin. These strata crop out in hogback ridges of the Utah-Idaho-Wyoming Thrust Belt approximately 40 km west of the crest of the Moxa Arch. Detailed, quantitative outcrop descriptions were constructed using emerging photogrammetric techniques along with field observations and measured sections at …


Geologic Mapping Of The Vernal Nw Quadrangle, Uintah County, Ut, And Stratigraphic Relationships Of The Duchesne River Formation And Bishop Conglomerate, Casey Andrew Webb Aug 2017

Geologic Mapping Of The Vernal Nw Quadrangle, Uintah County, Ut, And Stratigraphic Relationships Of The Duchesne River Formation And Bishop Conglomerate, Casey Andrew Webb

Theses and Dissertations

Detailed mapping (1:24,000), measured sections, and clast counts in conglomerates of the Duchesne River Formation and Bishop Conglomerate in the Vernal NW quadrangle in northeastern Utah reveal the middle Cenozoic stratigraphic geometry, the uplift and unroofing history of the eastern Uinta Mountains, and give evidence for the pulsed termination of Laramide uplift. The Unita Mountains are an EW-trending reverse fault bounded and basement-cored, Laramide uplift. The oldest unit of the Duchesne River Formation, the Eocene Brennan Basin Member, contains 80-90% Paleozoic clasts and <20% Precambrian clasts. Proximal to the Uinta uplift the conglomerates of this member are dominated by Paleozoic Madison Limestone clasts (70-90% of all clasts). Farther out into the basin, Paleozoic clasts still dominate in Brennan Basin Member conglomerates, but chert clasts are more abundant (up to 43%) showing the efficiency of erosion of the carbonate clasts over a short distance (~5 km). Conglomerates in the progressively younger Dry Gulch Creek, Lapoint, and Starr Flat members show a significant upward increase in Precambrian clasts with 34-73% Uinta Mountain Group and 8-63% Madison Limestone. Duchesne River Formation has a significant increase in coarse-grained deposits from the southern parts of the quadrangle (20-50% coarse) to the northern parts (75% coarse) nearer the Uinta uplift. The lower part of the Duchesne River Formation exhibits a fining upward sequence representing a tectonic lull. Clast count patterns show that pebbly channel deposits in the south maintain similar compositions to their alluvial fan counterparts. To the north, the fine-grained Lapoint and Dry Gulch Creek members of the Duchesne River Formation appear to pinch out completely. This can be explained by erosion of these fine-grained deposits or by lateral facies shifts before deposition of the next unit. Starr Flat Member conglomerates were deposited above Lapoint Member siltstones and represent southward progradation of alluvial fans away from the uplifting mountain front. Similarities in composition and sedimentary structures have caused confusion surrounding the contact between the Starr Flat Member and the overlying Bishop Conglomerate. Within the Vernal NW quadrangle, we interpret this contact as an angular unconformity (the Gilbert Peak Erosion Surface) developed on the uppermost tilted red siltstone of the Starr Flat Member sometime after 37.9 Ma. Stratigraphic and structural relationships reveal important details about the development of a Laramide mountain range: 1) sequential unroofing sequences in the Duchesne River Formation, 2) progradation of alluvial fans to form the Starr Flat Member, 3) and the unconformable nature of the Gilbert Peak Erosion Surface lead to the conclusion that there were at least 3 distinct episodes of uplift during the deposition of these formations. The last uplift episode upwarped the Starr Flat Member constraining the termination of Laramide uplift in the Uinta Mountains to be after deposition of the Starr Flat Member and prior to deposition of the horizontal Bishop Conglomerate starting at about 34 Ma. This, combined with 40Ar/39Ar ages of 39.4 Ma from the Dry Gulch Creek and Lapoint member, show …


Improving Gamification By Leveraging Endogenous Value, Brennan Laurence Smith Aug 2017

Improving Gamification By Leveraging Endogenous Value, Brennan Laurence Smith

Theses and Dissertations

"Gamification" is the application of game design principles to non-game contexts, such as education, personal fitness, etc. Gamification's intent is to incentivize unpalatable tasks. Current gamification efforts in the industry use some features traditionally associated with games, but fail to use game design principles as defined by the games industry. One such principle is endogenous rewards for task completion. We propose that endogenous rewards will increase the efficacy of gamification by increasing user engagement and retention. To demonstrate, we create a gamification framework where the rewards for completing real-life tasks are items with high endogenous value in the game, incentivizing …


Custom 3d Printer And Resin For 18 Μm × 20 Μm Mi- Crofluidic Flow Channels, Hua Gong, Bryce P. Bickham, Adam T. Woolley, Gregory P. Nordin Jul 2017

Custom 3d Printer And Resin For 18 Μm × 20 Μm Mi- Crofluidic Flow Channels, Hua Gong, Bryce P. Bickham, Adam T. Woolley, Gregory P. Nordin

Faculty Publications

While there is great interest in 3D printing for microfluidic device fabrication, to-date the achieved feature sizes have not been in the truly microfluidic regime (μm). In this paper we demonstrate that a custom Digital Light Processor stereolithographic (DLP-SLA) 3D printer and a specifically-designed, low cost, custom resin can readily achieve flow channel cross sections as small as 18 μm × 20 μm. Our 3D printer has a projected image plane resolution of 7.6 μm and uses a 385 nm LED, which dramatically increases the available selection of UV absorbers for resin formulation compared to 3D printers with 405 nm …


Limitations In The Reproductive Success Of A Burrow-Nesting Bird (Momotus Mexicanus) During A Humid Season, Grégory Michaël Charre, Omar Paniagua, Marcela Osorio-Beristain Jul 2017

Limitations In The Reproductive Success Of A Burrow-Nesting Bird (Momotus Mexicanus) During A Humid Season, Grégory Michaël Charre, Omar Paniagua, Marcela Osorio-Beristain

Western North American Naturalist

Burrow-nesting birds are limited by access to nest sites, particularly in years of very high humidity levels, such those seen with El Niño, or in forests that are fragmented due to the effects of human activity. We assessed the breeding success of Momotus mexicanus nesting along the earth bank of a secondary road corridor in a seasonally dry tropical forest in Central Mexico. We monitored 28 nests during the reproductive period and characterized the composition of the soil where they were constructed, as well as other physical variables. One nest produced 2 fledglings, and the other 27 failed to …


Desert Wildfire Impacts On Ant And Small Mammal Communities And Its Consequences For Plant Invasions, Sam St. Clair Jul 2017

Desert Wildfire Impacts On Ant And Small Mammal Communities And Its Consequences For Plant Invasions, Sam St. Clair

Journal of Undergraduate Research

We successfully completed the studies as outlined in the proposal and the data collected. The results have been written up a in a successfully defended MS thesis with three chapters (Tiffany Sharp) and another MS student is currently writing their thesis (Josh Day). Six undergraduate students completed mentored research credit and were paid to work on the project.


Unleashing The Power Of Undergraduates To Unravel The Impacts Of Water Relations And Co2 Levels On The Photosynthetic Plasticity Of Agave Sensu Lato Species: A Group Of Desert Succulents Important To Natural And Human Systems, J. Ryan Stewart Jul 2017

Unleashing The Power Of Undergraduates To Unravel The Impacts Of Water Relations And Co2 Levels On The Photosynthetic Plasticity Of Agave Sensu Lato Species: A Group Of Desert Succulents Important To Natural And Human Systems, J. Ryan Stewart

Journal of Undergraduate Research

  • Evaluation of how well the academic objectives of the proposal were met
  • Evaluation of the mentoring environment
  • List of students who participated and what academic deliverables they have produced or it is anticipated they will produce
  • Description of the results/findings of the project
  • Description of how the budget was spent


Improved Leaky-Mode Waveguide Spatial Light Modulators For Three Dimensional Displays, Scott Alexander Gneiting Jul 2017

Improved Leaky-Mode Waveguide Spatial Light Modulators For Three Dimensional Displays, Scott Alexander Gneiting

Theses and Dissertations

This thesis improves on the design of the leaky-mode spatial light modulator, LMW-SLM, presented by Dr. Smalley[1]. Improvements include: input coupling gratings, a pulsed laser input, output coupling gratings, and a 3D printed adjustable module for the stabilization of critical alignments. First, input coupling gratings reduce the cost of the LMW-SLM from $500 to around $2, a drop in cost of over two orders of magnitude. This enables multiple modulators to be used in a single display and allows for an inexpensive modular design to be created. Second, a pulsed laser input allows for image creation without the use of …


Acylation Of Superoxide Dismutase 1 (Sod1) At K122 Alters Sod1 Localization And Sod1-Mediated Inhibition Of Mitochondrial Respiration, Nathan William Rodriguez Jul 2017

Acylation Of Superoxide Dismutase 1 (Sod1) At K122 Alters Sod1 Localization And Sod1-Mediated Inhibition Of Mitochondrial Respiration, Nathan William Rodriguez

Theses and Dissertations

Cu/Zn Superoxide Dismutase (SOD1), is a ubiquitous antioxidant enzyme with several emerging roles outside of its canonical function. SOD1 is also emerging in central roles in cancer and neurodegenerative pathologies. Little is known about SOD1 regulation, particularly at a post-translational level. Post-translational modifications (PTMs) play an important role in enabling proteins to rapidly respond to their environment. Therefore, identifying specific PTMs involved in protein regulation represents a powerful opportunity to interfere with any associated pathologies. This work employs proteomics to identify mechanisms of post-translation regulation on cell survival signaling proteins. We focused on SOD1, which protects cells from oxidative stress. …


Perceived Effects Of Open Textbook Usage On Secondary Science Classroom Practice, Stacie Lee Mason Jul 2017

Perceived Effects Of Open Textbook Usage On Secondary Science Classroom Practice, Stacie Lee Mason

Theses and Dissertations

Open Educational Resources (OER) provide openly licensed alternatives to commercial instructional materials. Proponents of K-12 OER suggest that their benefits include cost savings, increased access, improved quality, and increased teacher professionalism or empowerment. While the small body of K-12 OER research is growing, perceived benefits of K-12 OER usage have not yet been proven. The purpose of this qualitative study is to understand whether certain potential benefits were being realized by a group of secondary teachers using open science textbooks. In surveys and interviews, teachers were asked to describe their classroom practice before and after adopting an open textbook, including …


Utility Of Feedback Given By Students During Courses, Michael Alton Atkisson Jul 2017

Utility Of Feedback Given By Students During Courses, Michael Alton Atkisson

Theses and Dissertations

This two-article dissertation summarizes the end-of-course survey and formative feedback literatures, as well as proposes actionability as a useful construct in the analysis of feedback from students captured in real-time during their courses. The present inquiry grew out of my work as the founder of DropThought Education, a Division of DropThought. DropThought Education was a student feedback system that helped instructional designers, instructors, and educational systems to use feedback from students to improve learning and student experience. To find out whether the DropThought style of feedback was more effective than other forms of capturing and analyzing student feedback, I needed …


Adapting Dracula: The Afterlives Of Stoker's Memes In Nosferatu (1922) And Dracula (1979), Ian Duncan Mcarthur Jul 2017

Adapting Dracula: The Afterlives Of Stoker's Memes In Nosferatu (1922) And Dracula (1979), Ian Duncan Mcarthur

Theses and Dissertations

Dracula is a narrative that has risen above its own origins, having been translated and adapted across mediums it has inundated culture with vampires. However, with each adaptation the narrative and characters adapt into something new. This study is interested in the mechanism behind this evolution and argues that memes and, and their interpretations, are largely responsible for these shifts across adaptations. Three memes, in particular, tend to be adapted in films of Dracula. They include Dracula's appearance, Mina's empowerment, and the nature of the bite that they share. This analysis covers how these memes functioned in Stoker's original …


Spaces Of Weakly Holomorphic Modular Forms In Level 52, Daniel Meade Adams Jul 2017

Spaces Of Weakly Holomorphic Modular Forms In Level 52, Daniel Meade Adams

Theses and Dissertations

Let M#k(52) be the space of weight k level 52 weakly holomorphic modular forms with poles only at infinity, and S#k(52) the subspace of forms which vanish at all cusps other than infinity. For these spaces we construct canonical bases, indexed by the order of vanishing at infinity. We prove that the coefficients of the canonical basis elements satisfy a duality property. Further, we give closed forms for the generating functions of these basis elements.


Weakly Holomorphic Modular Forms In Level 64, Christopher William Vander Wilt Jul 2017

Weakly Holomorphic Modular Forms In Level 64, Christopher William Vander Wilt

Theses and Dissertations

Let M#k(64) be the space of weakly holomorphic modular forms in level 64 and weight k which can have poles only at infinity, and let S#k(64) be the subspace of M#k(64) consisting of forms which vanish at all cusps other than infinity. We explicitly construct canonical bases for these spaces and show that the coefficients of these basis elements satisfy Zagier duality. We also compute the generating function for the canonical basis.


Teacher Response To Instances Of Student Thinking During Whole Class Discussion, Rachel Marie Bernard Jul 2017

Teacher Response To Instances Of Student Thinking During Whole Class Discussion, Rachel Marie Bernard

Theses and Dissertations

While the use of student thinking to help build mathematical understandings in a classroom has been emphasized in best teaching practices, teachers still struggle with this practice and research still lacks a full understanding of how such learning can and should occur. To help understand this complex practice, I analyzed every instance of student thinking and every teacher response to that thinking during a high school geometry teacher's whole class discussion and used these codes as evidence of alignment or misalignment with principles of effective use of student mathematical thinking. I explored the teacher's practice both in small and large …